A level set formulation for Willmore flow

A level set formulation of Willmore flow is derived using the gradient flow perspective. Starting from single embedded surfaces and the corresponding gradient flow, the metric is generalized to sets of level set surfaces using the identification of normal velocities and variations of the level set function in time via the level set equation. This approach in particular allows one to identify the natural dependent quantities of the derived variational formulation. Furthermore, spatial and temporal discretizations are discussed and some numerical simulations are presented.